I don't think the sense of "balances" is financial here. I believe that in this context it refers to the relationship between supply and demand in the oil market. A tightening or constriction of balances means a restriction of supply compared to demand. To say that the oil market is tightening means that supply is relatively restricted relative to demand, which of course pushes prices up. This has been happening for several reasons: economic growth, cold weather and cuts in production (particularly in Venezuela). The price could rise as high as $80 a barrel. The US withdrawal from the nuclear deal with Iran will further tighten (supply/demand) balances because it will reduce supply: Iranian exports will be cut. So how constricted these balances become will depend on how OPEC (and Russian) respond: whether and how much they increase production to compensate.

The following is from January this year, before the Iran news:

"“We have updated our supply/demand balances to reflect a faster-than-expected tightening in the global oil market due to improving cyclical conditions, cold winter weather, and higher than expected OPEC compliance,” Bank of America Merrill Lynch said.
[OPEC compliance means OPEC countries' compliance with production cuts.]
In an effort to tighten markets and prop up prices, the Organization of the Petroleum Exporting Countries (OPEC) and Russia started to withhold production in January last year, and the cuts are set to last through 2018."
https://www.reuters.com/article/global-oil/oil-markets-near-...

So tighter oil balances means higher demand relative to supply (or lower supply relative to demand):

"Global production and consumption are both projected to increase through 2018, but consumption is expected to increase at a faster rate than production. As a result, global balances are expected to tighten."
https://www.eia.gov/todayinenergy/detail.php?id=29672

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Note added at 51 mins (2018-05-15 00:46:27 GMT)
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"Tight balances will support crude prices": because if the balances are tight it means that supply is restricted relative to demand, and in that situation prices rise.

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Note added at 1 hr (2018-05-15 01:05:29 GMT)
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There are a number of documents that show that the term "oil balances" refers to the balance between supply and demand. For example:

"Over the last few months, the oil market has remained fixated on global oil supply. There have been several debates on OPEC vs Shale and the duration of OPEC production cuts.
However, global oil demand continues to receive very little attention despite it being the other half of global oil balances."
https://seekingalpha.com/article/4058092-global-oil-demand-g...